Inhomogeneous state of the electron system in the $\mathrm{Sr}_{14-x}\mathrm{Ca}_x\mathrm{Cu_{24}O_{41}}$ superconducting cuprate: $^{63}\mathrm{Cu}$, $^{17}\mathrm O$ NMR study

Charge fluctuations in quasi-one-dimensional hole-doped Sr₁₄Cu₂₄O₄₁ (Ca-0) and Sr₂Ca₁₂Cu₂₄O₄₁ (Ca-12) spin-ladder cuprates have been studied with the use of ⁶³Cu-¹⁷O NMR. Spin-echo decay rates ¹⁷(1/T ₂) and ⁶³(1/T ₂) have been measured in the temperature range of T = 10–300 K. The variation of ¹⁷(1/T ₂) and ⁶³(1/T ₂) in the Ca-0 compound is monotonic in the entire temperature range of the NMR study. In the Ca-rich compound, pronounced peaks have been observed in the decay rates ¹⁷(1/T ₂) and ⁶³(1/T ₂) at temperatures of 25 and 50 K, respectively. This result indicates the presence of collective low-frequency (τ_c ~ T ₂) charge density fluctuations in superconducting Ca-12 with an activation energy of E _A = 100(10) K. The fluctuations gradually slow down as the temperature decreases. The amplitude of the charge density fluctuations is only 0.01–0.02 hole per site. ¹⁷O-⁶³Cu spin-echo double-resonance (SEDOR) experiments in Sr_{14 − x} Ca _x Cu₂₄O₄₁ oxides with x = 0 and 12 have been performed depending on the temperature and orientation of single crystals in a magnetic field. The constants of an indirect heteronuclear ¹⁷O-⁶³Cu interaction of nuclear spins mediated by conduction electrons have been measured. The estimates of the indirect interaction constants for nearest neighbors O1-Cu and O2-Cu, as well as SEDOR experiments with selective excitation of separate sections of ¹⁷O and ⁶³Cu NMR spectra, provide convincing evidence of the microscopically inhomogeneous spatial distribution of spin density developing in a crystal.